FV1 = P0 (1 + i)1 = $1,000 (1.07) = $1,070 - FV1 = P0 (1 + i)1 = $1,000 (1.07) = $1,070
- FV2 = FV1 (1 + i)1 = P0 (1 + i)(1 + i) = $1,000(1.07)(1.07) = P0 (1 + i)2 = $1,000(1.07)2 = $1,144.90
- You earned an EXTRA $4.90 in Year 2 with compound over simple interest.
- Future Value
- Single Deposit (Formula)
- FV1 = P0(1 + i)1
- FV2 = P0(1 + i)2
- General Future Value Formula:
- FVn = P0 (1 + i)n
- or FVn = P0 (FVIFi,n) – See Table I
Valuation Using Table I - FVIFi,n is found on Table I
- at the end of the book.
Using Future Value Tables - FV2 = $1,000 (FVIF7%,2) = $1,000 (1.145) = $1,145 [Due to Rounding]
TVM on the Calculator - N: Number of periods
- I/Y: Interest rate per period
- PV: Present value
- PMT: Payment per period
- FV: Future value
- CLR TVM: Clears all of the inputs into the above TVM keys
Using The TI BAII+ Calculator - Focus on 3rd Row of keys (will be displayed in slides as shown above)
- Press:
- 2nd CLR TVM
- 2 N
- 7 I/Y
- –1000 PV
- 0 PMT
- CPT FV
- Source: Courtesy of Texas Instruments
Solving the FV Problem - N: 2 Periods (enter as 2)
- I/Y: 7% interest rate per period (enter as 7 NOT 0.07)
- PV: $1,000 (enter as negative as you have “less”)
- PMT: Not relevant in this situation (enter as 0)
- FV: Compute (Resulting answer is positive)
- Julie Miller wants to know how large her deposit of $10,000 today will become at a compound annual interest rate of 10% for 5 years.
Story Problem Solution - Calculation based on Table I: FV5 = $10,000 (FVIF10%, 5) = $10,000 (1.611) = $16,110 [Due to Rounding]
- Calculation based on general formula: FVn = P0 (1 + i)n FV5 = $10,000 (1 + 0.10)5 = $16,105.10
Entering the FV Problem - Press:
- 2nd CLR TVM
- 5 N
- 10 I/Y
- –10000 PV
- 0 PMT
- CPT FV
- Source: Courtesy of Texas Instruments
Solving the FV Problem - The result indicates that a $10,000 investment that earns 10% annually for 5 years will result in a future value of $16,105.10.
Double Your Money!!! - We will use the “Rule-of-72”.
- Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?
The “Rule-of-72” - Approx. Years to Double = 72 / i%
- 72 / 12% = 6 Years
- [Actual Time is 6.12 Years]
- Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?
Solving the Period Problem - The result indicates that a $1,000 investment that earns 12% annually will double to $2,000 in 6.12 years.
- Note: 72/12% = approx. 6 years
Present Value Single Deposit (Graphic) - Assume that you need $1,000 in 2 years. Let’s examine the process to determine how much you need to deposit today at a discount rate of 7% compounded annually.
PV0 = FV2 / (1 + i)2 = $1,000 / (1.07)2 = FV2 / (1 + i)2 = $873.44 - PV0 = FV2 / (1 + i)2 = $1,000 / (1.07)2 = FV2 / (1 + i)2 = $873.44
- Present Value Single Deposit (Formula)
PV0 = FV1 / (1 + i)1 - PV0 = FV1 / (1 + i)1
- PV0 = FV2 / (1 + i)2
- General Present Value Formula:
- PV0 = FVn / (1 + i)n
- or PV0 = FVn (PVIFi,n) – See Table II
- General Present Value Formula
- PV2 = $1,000 (PVIF7%,2) = $1,000 (.873) = $873 [Due to Rounding]
- Using Present Value Tables
- N: 2 Periods (enter as 2)
- I/Y: 7% interest rate per period (enter as 7 NOT 0.07)
- PV: Compute (Resulting answer is negative “deposit”)
- PMT: Not relevant in this situation (enter as 0)
- FV: $1,000 (enter as positive as you “receive $”)
Julie Miller wants to know how large of a deposit to make so that the money will grow to $10,000 in 5 years at a discount rate of 10%. - Julie Miller wants to know how large of a deposit to make so that the money will grow to $10,000 in 5 years at a discount rate of 10%.
Calculation based on general formula: PV0 = FVn / (1 + i)n PV0 = $10,000 / (1 + 0.10)5 = $6,209.21 - Calculation based on general formula: PV0 = FVn / (1 + i)n PV0 = $10,000 / (1 + 0.10)5 = $6,209.21
- Calculation based on Table I: PV0 = $10,000 (PVIF10%, 5) = $10,000 (0.621) = $6,210.00 [Due to Rounding]
- The result indicates that a $10,000 future value that will earn 10% annually for 5 years requires a $6,209.21 deposit today (present value).
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